HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 10: Correlation. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 5/5/2014 , Spring 2014. Final Exam. Monday 5/19/2014 Time and Place of the class Chapters 9, 10 and 11

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## HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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• Chapter 10: Correlation

### HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D.

5/5/2014, Spring 2014

Final Exam
• Monday 5/19/2014
• Time and Place of the class
• Chapters 9, 10 and 11
• Same format as past two exams
• No re-submission of homework
• Summer SAS Course
Learning Objectives
• After this lecture, you should be able to complete the following Learning Outcomes
• 10.1
10.1Correlation

Until now, we’ve examined the presence or absence of a relationship between two or more variables

What about the strength and direction of this relationship?

• We refer to this as the correlation between variables

Strength of Correlation

• This can be visualized using a scatter plot
• Strength increases as the points more closely form an imaginary diagonal line across the center

Direction of Correlation

• Correlations can be described as either positive or negative
• Positive – both variables move in the same direction
• Negative – the variables move in opposite directions

10.1

Figure 10.1

10.1

Figure 10.2

Learning Objectives
• After this lecture, you should be able to complete the following Learning Outcomes
• 10.2
Identify a curvilinear correlation
10.2Curvilinear Correlation

A relationship between X and Y that begins as positive and becomes negative, or begins as negative and becomes positive

Figure 10.3

Learning Objectives
• After this lecture, you should be able to complete the following Learning Outcomes
• 10.3
Discuss the characteristics of correlation coefficients
10.3The Correlation Coefficient

Numerically expresses both the direction and strength of a relationship between two variables

• Ranges between -1.0 and + 1.0

Direction

• Strength
• The sign (either – or +) indicates the direction of the relationship
• Values close to zero indicate little or no correlation
• Values closer to -1 or +1, indicate stronger correlations
Learning Objectives
• After this lecture, you should be able to complete the following Learning Outcomes
• 10.4
Calculate and test the significance of Pearson’s correlation coefficient (r)
10.4Pearson’s Correlation Coefficient (r)

Focuses on the product of the X and Y deviations from their respective means

• Deviations Formula:
• Computational Formula:
10.4Testing the Significance of Pearson’s r

The null hypothesis states that no correlation exists in the population (ρ = 0)

• To test the significance of r, at ratio with degrees of freedom N – 2 must be calculated

A simplified method for testing the significance of r

• Compare the calculated r to a critical value found in Table H in Appendix C
Exercises

Problem 6, 19, 21

10.4
• A Straight-Line Relationship
• Interval Data
• Random Sampling
• Normally Distributed Characteristics
Learning Objectives
• After this lecture, you should be able to complete the following Learning Outcomes
• 10.5
Calculate the partial correlation coefficient
10.5Partial Correlation

The correlation between two variables, X and Y, after removing the common effects of a third variable, Z

When testing the significance of a partial correlation, a slightly different t formula is used

Exercise

Problem 30

Homework

Problems 18, 22 and 31

CHAPTER SUMMARY

• Correlation allows researchers to determine the strength and direction of the relationship between two or more variables

10.1

• In a curvilinear correlation, the relationship between two variables starts out positive and turns negative, or vice versa

10.2

• The correlation coefficient numerically expresses the direction and strength of a linear relationship between two variables

10.3

• Pearson’s correlation coefficient can be calculated for two interval-level variables

10.4

• The partial correlation coefficient can be used to examine the relationship between two variables, after removing the common effect of a third variable

10.5